Problem: Simplify the following expression: $\sqrt{176}-\sqrt{275}+\sqrt{44}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{176}-\sqrt{275}+\sqrt{44}$ $= \sqrt{16 \cdot 11}-\sqrt{25 \cdot 11}+\sqrt{4 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{11}-\sqrt{25} \cdot \sqrt{11}+\sqrt{4} \cdot \sqrt{11}$ $= 4\sqrt{11}-5\sqrt{11}+2\sqrt{11}$ Finally, simplify by combining the terms. $= ( 4 - 5 + 2 )\sqrt{11} = \sqrt{11}$